The drawing below (not to scale) shows a running track. The ends are semicircles. The distance between the two inner parallel st
raight lines is 60 meters, and they are each 100 meters long. The track is 10 meters wide. Find the area of the actual track (the shaded region).
1 answer:
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We know from Euclidean Geometry and the properties of a centroid that GC=2GM. Now GM=sin60*GA=
. Hence CM=GC+GM=3*
. Now, since GM is normal to AB, we have by the pythagoeran theorem that:
Hence, we calculate from this that AC^2= 28, hence AC=2*
=BC. Thus, the perimeter of the triangle is 2+4*.
Hence, we calculate from this that AC^2= 28, hence AC=2*